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  1. Home
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  3. Lectures on the Ricci Flow
  • Cited by 125
Publisher:
Cambridge University Press
Online publication date:
May 2010
Print publication year:
2006
Online ISBN:
9780511721465
DOI:
https://doi.org/10.1017/CBO9780511721465
Subjects:
Mathematics (general), Mathematics, Geometry and Topology
Series:
London Mathematical Society Lecture Note Series (325)
Information

Book description

Hamilton's Ricci flow has attracted considerable attention since its introduction in 1982, owing partly to its promise in addressing the Poincaré conjecture and Thurston's geometrization conjecture. This book gives a concise introduction to the subject with the hindsight of Perelman's breakthroughs from 2002/2003. After describing the basic properties of, and intuition behind the Ricci flow, core elements of the theory are discussed such as consequences of various forms of maximum principle, issues related to existence theory, and basic properties of singularities in the flow. A detailed exposition of Perelman's entropy functionals is combined with a description of Cheeger-Gromov-Hamilton compactness of manifolds and flows to show how a 'tangent' flow can be extracted from a singular Ricci flow. Finally, all these threads are pulled together to give a modern proof of Hamilton's theorem that a closed three-dimensional manifold whichcarries a metric of positive Ricci curvature is a spherical space form.

Reviews

"... The freedom to skip some of the proofs, and the lucid presentation, this small book is pleasant to read."
Peng Lu, Mathematical Reviews

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